# Properties of atomic pairs produced in the collision of Bose-Einstein condensates

## TL;DR

This paper investigates atomic pair correlations resulting from Bose-Einstein condensate collisions, deriving analytical and numerical tools to understand their quantum properties and potential for nonclassicality demonstrations.

## Contribution

It provides a detailed Bogoliubov-based analysis of atomic correlations in condensate collisions, including new analytical expressions and a semiclassical model.

## Key findings

- Derived explicit formulas for one and two-particle correlation functions.
- Compared quantum and semiclassical models, highlighting their differences.
- Results are applicable to recent helium atom experiments and future nonclassicality tests.

## Abstract

Collisions of Bose-Einstein condensates can be used as a mean to generate correlated pairs of atoms. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of Einstein-Podolsky-Rosen correlations, or sub-shot noise atomic interferometry. Usually, a theoretical description of the collision relies either on stochastic numerical methods or on analytical treatments involving various approximations. Here, we investigate elastic scattering of atoms from colliding elongated Bose-Einstein condensates within Bogoliubov method, carefully controlling performed approximations at every stage of the analysis. We derive expressions for the one and two particle correlation functions. The obtained formulas, which relate the correlation functions with condensate wavefunction, are convenient for numerical calculations. We employ variational approach for condensate wavefunctions to obtain analytical expressions for the correlation functions, which properties we analyze in details. We also present a useful semiclassical model of the process, and compare its results with the quantum one. The results are relevant for recent experiments with excited helium atoms, as well as for planned experiments aimed at investigating the nonclassicality of the system.